Mathematics

Problem

Let

P

be an

m \times n

matrix,

Q

n \times 3

matrix and

R

a matrix such that the expression

PQ+R

is defined. Suppose further that

m=4

and

n=5

. a. (i) Determine the order of

PQ

. b. (ii) Using the fact that

PQ+R

is a valid sum, find the order of

R

. c. (iii) Compute the total number of elements in each of the matrices

PQ

and

PQ+R

. d. (iv) For these values of

m

and

n

, compare the number of elements in

R

with that in

P

, and state which matrix contains more elements.